What is Algorithm?

Algorithms are the recipes of computing. Just as a cooking recipe tells you step-by-step how to prepare a dish, an algorithm tells a computer exactly what steps to follow to accomplish a goal. Every piece of software, from a simple calculator to a complex AI system, executes algorithms at its core.

What Makes Something an Algorithm

A proper algorithm has several defining characteristics. It must have a finite number of steps (it terminates). It must have well-defined inputs and outputs. Each step must be unambiguous, leaving no room for interpretation. And it must be effective, meaning each step can actually be carried out. These properties distinguish algorithms from vague instructions or open-ended processes.

Algorithms predate computers. The word itself comes from the name of the 9th-century Persian mathematician Muhammad ibn Musa al-Khwarizmi. Euclid's algorithm for finding the greatest common divisor of two numbers dates to around 300 BCE. What computers add is the ability to execute algorithms billions of times per second on vast amounts of data, making algorithms that would be impractical by hand enormously powerful in practice.

Algorithms in Machine Learning

In machine learning, algorithms are the methods used to train models. The training process is itself an algorithm: take data as input, adjust model parameters according to a learning rule, and output a trained model. Different learning tasks use different algorithms, each with distinct strengths and tradeoffs.

The gradient descent algorithm is perhaps the most important in modern AI. It is used to adjust the weights in a neural network to reduce prediction errors during training. The algorithm computes how much each weight contributes to the overall error (using calculus), then adjusts each weight in the direction that reduces the error. Repeated over millions of iterations on large datasets, this simple algorithm produces the deep learning models that power modern AI.

Backpropagation is the algorithm that makes gradient descent efficient for deep neural networks. It computes gradients layer by layer, starting from the output and working backward through the network (hence 'back-propagation'), avoiding redundant calculations that would make training impractically slow.

Classical ML algorithms include decision trees (recursive splitting rules that create interpretable if-then logic), random forests (ensembles of many decision trees that vote on the answer), support vector machines (finding optimal boundaries between classes), k-nearest neighbors (classifying by similarity to labeled examples), and k-means clustering (grouping data points by proximity). Each has different characteristics in terms of accuracy, speed, interpretability, and data requirements.

Algorithm Efficiency: Time and Space Complexity

The quality of an algorithm matters enormously, and quality is often measured by efficiency. Two algorithms might solve the same problem, but one could be thousands or millions of times faster than the other on large datasets. Computer scientists analyze efficiency using Big O notation, which describes how an algorithm's running time or memory usage grows as the input size increases.

An algorithm with O(n) time complexity processes each item once, scaling linearly with data size. An algorithm with O(n^2) processes each pair of items, becoming impractical for large datasets. An algorithm with O(log n) barely slows down as data grows (binary search is an example). Understanding these distinctions helps explain why some AI operations that seem simple (like finding similar items in a large dataset) require sophisticated algorithms and data structures like vector databases to work at scale.

In AI, the efficiency of training and inference algorithms directly determines what is practical. The attention mechanism in transformers has O(n^2) complexity with respect to sequence length, which is why processing very long documents is expensive. Research into more efficient attention algorithms (linear attention, sparse attention, sliding window attention) is driven by the need to reduce this computational cost.

Search and Optimization Algorithms

Many AI problems are fundamentally search or optimization problems. Search algorithms find solutions in large spaces of possibilities. A chess-playing AI searches through millions of possible future board states to find the best move. A route-planning algorithm searches through millions of possible paths to find the shortest one.

Optimization algorithms find the best parameters for a given objective. Gradient descent is the most famous optimization algorithm in AI, but there are many others: Adam (adaptive learning rates), SGD with momentum, RMSprop, and evolutionary algorithms that mimic natural selection. Reinforcement learning uses optimization algorithms to find the best policy (strategy) for an agent acting in an environment.

Heuristic algorithms find good-enough solutions when finding the perfect solution is computationally infeasible. Many real-world AI problems are too complex for exact solutions, so heuristic approaches that trade optimality for speed are essential.

Algorithms and Fairness

Algorithms also raise important ethical questions. When an algorithm decides who gets a loan, whose resume gets reviewed, what news appears in your feed, what content gets recommended, or what price you see for a product, the logic embedded in those decisions has real-world consequences. This is why algorithmic fairness and responsible AI practices are increasingly important fields of study and regulation.

Algorithmic bias can enter at multiple points: through biased training data, through objective functions that optimize for metrics that do not capture fairness, through feedback loops where algorithmic decisions influence future data, or through design choices that disproportionately affect certain groups. Detecting and mitigating these biases requires deliberate effort and is the subject of a growing body of research and regulation, including the EU AI Act.

Algorithms in Everyday AI Tools

For everyday professionals, algorithms work silently in the background of the tools they use. The recommendation systems that suggest products use collaborative filtering and content-based algorithms. The spam filters that clean up inboxes use classification algorithms. The AI copilots that help draft emails use language model inference algorithms. Search engines use ranking algorithms to determine which results are most relevant. Navigation apps use graph traversal algorithms to find the fastest route.

Engineering copilots help developers implement algorithms correctly and efficiently. AI/ML copilots assist data scientists in selecting the right algorithms for their specific problems. Understanding what algorithms are and how they differ is foundational to making good decisions about AI tools and systems.

Historical Context

Algorithms have been central to mathematics for millennia, but the formal study of algorithms as a field of computer science began in the mid-20th century with the work of Alan Turing, John von Neumann, and Donald Knuth. Knuth's multi-volume The Art of Computer Programming (begun in 1968) remains a foundational reference. The development of machine learning algorithms accelerated in the 1980s and 1990s, and the deep learning revolution since 2012 has produced a new generation of training and optimization algorithms that underpin modern AI.

Why Algorithms Matter in 2026

Algorithms remain the intellectual core of computer science and AI. As AI systems become more powerful and pervasive, the algorithms that drive them become more consequential. Understanding algorithms at a conceptual level, what they optimize for, what tradeoffs they make, and what biases they might introduce, is increasingly important for everyone who uses or is affected by AI systems.

Explore related concepts including machine learning, gradient descent, neural networks, and algorithmic fairness in the AI Glossary. For practical AI tools, explore Copilotly's professional copilots. For academic depth, MIT's Introduction to Algorithms (CLRS) is the standard textbook, and Stanford's AI courses cover algorithms in the context of machine learning and artificial intelligence.